Properties

Label 2646.2.h.q.667.4
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 882)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.4
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.q.361.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.93185 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.93185 q^{5} +1.00000 q^{8} +(-0.965926 - 1.67303i) q^{10} -5.46410 q^{11} +(-1.22474 - 2.12132i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(3.15660 + 5.46739i) q^{17} +(0.965926 - 1.67303i) q^{19} +(-0.965926 + 1.67303i) q^{20} +(2.73205 + 4.73205i) q^{22} +5.92820 q^{23} -1.26795 q^{25} +(-1.22474 + 2.12132i) q^{26} +(-0.366025 + 0.633975i) q^{29} +(3.67423 - 6.36396i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.15660 - 5.46739i) q^{34} +(4.00000 - 6.92820i) q^{37} -1.93185 q^{38} +1.93185 q^{40} +(2.82843 + 4.89898i) q^{41} +(0.901924 - 1.56218i) q^{43} +(2.73205 - 4.73205i) q^{44} +(-2.96410 - 5.13397i) q^{46} +(-4.76028 - 8.24504i) q^{47} +(0.633975 + 1.09808i) q^{50} +2.44949 q^{52} +(1.63397 + 2.83013i) q^{53} -10.5558 q^{55} +0.732051 q^{58} +(2.50026 - 4.33057i) q^{59} +(1.48356 + 2.56961i) q^{61} -7.34847 q^{62} +1.00000 q^{64} +(-2.36603 - 4.09808i) q^{65} +(7.09808 - 12.2942i) q^{67} -6.31319 q^{68} +11.1962 q^{71} +(-4.76028 - 8.24504i) q^{73} -8.00000 q^{74} +(0.965926 + 1.67303i) q^{76} +(5.06218 + 8.76795i) q^{79} +(-0.965926 - 1.67303i) q^{80} +(2.82843 - 4.89898i) q^{82} +(-4.94975 + 8.57321i) q^{83} +(6.09808 + 10.5622i) q^{85} -1.80385 q^{86} -5.46410 q^{88} +(6.64136 - 11.5032i) q^{89} +(-2.96410 + 5.13397i) q^{92} +(-4.76028 + 8.24504i) q^{94} +(1.86603 - 3.23205i) q^{95} +(-1.93185 + 3.34607i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + O(q^{10}) \) \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{11} - 4 q^{16} + 8 q^{22} - 8 q^{23} - 24 q^{25} + 4 q^{29} - 4 q^{32} + 32 q^{37} + 28 q^{43} + 8 q^{44} + 4 q^{46} + 12 q^{50} + 20 q^{53} - 8 q^{58} + 8 q^{64} - 12 q^{65} + 36 q^{67} + 48 q^{71} - 64 q^{74} - 8 q^{79} + 28 q^{85} - 56 q^{86} - 16 q^{88} + 4 q^{92} + 8 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.93185 0.863950 0.431975 0.901886i \(-0.357817\pi\)
0.431975 + 0.901886i \(0.357817\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.965926 1.67303i −0.305453 0.529059i
\(11\) −5.46410 −1.64749 −0.823744 0.566961i \(-0.808119\pi\)
−0.823744 + 0.566961i \(0.808119\pi\)
\(12\) 0 0
\(13\) −1.22474 2.12132i −0.339683 0.588348i 0.644690 0.764444i \(-0.276986\pi\)
−0.984373 + 0.176096i \(0.943653\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.15660 + 5.46739i 0.765587 + 1.32604i 0.939936 + 0.341352i \(0.110885\pi\)
−0.174349 + 0.984684i \(0.555782\pi\)
\(18\) 0 0
\(19\) 0.965926 1.67303i 0.221599 0.383820i −0.733695 0.679479i \(-0.762206\pi\)
0.955294 + 0.295659i \(0.0955392\pi\)
\(20\) −0.965926 + 1.67303i −0.215988 + 0.374101i
\(21\) 0 0
\(22\) 2.73205 + 4.73205i 0.582475 + 1.00888i
\(23\) 5.92820 1.23612 0.618058 0.786133i \(-0.287920\pi\)
0.618058 + 0.786133i \(0.287920\pi\)
\(24\) 0 0
\(25\) −1.26795 −0.253590
\(26\) −1.22474 + 2.12132i −0.240192 + 0.416025i
\(27\) 0 0
\(28\) 0 0
\(29\) −0.366025 + 0.633975i −0.0679692 + 0.117726i −0.898007 0.439981i \(-0.854985\pi\)
0.830038 + 0.557707i \(0.188319\pi\)
\(30\) 0 0
\(31\) 3.67423 6.36396i 0.659912 1.14300i −0.320726 0.947172i \(-0.603927\pi\)
0.980638 0.195829i \(-0.0627398\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 3.15660 5.46739i 0.541352 0.937649i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000 6.92820i 0.657596 1.13899i −0.323640 0.946180i \(-0.604907\pi\)
0.981236 0.192809i \(-0.0617599\pi\)
\(38\) −1.93185 −0.313388
\(39\) 0 0
\(40\) 1.93185 0.305453
\(41\) 2.82843 + 4.89898i 0.441726 + 0.765092i 0.997818 0.0660290i \(-0.0210330\pi\)
−0.556092 + 0.831121i \(0.687700\pi\)
\(42\) 0 0
\(43\) 0.901924 1.56218i 0.137542 0.238230i −0.789024 0.614363i \(-0.789413\pi\)
0.926566 + 0.376133i \(0.122746\pi\)
\(44\) 2.73205 4.73205i 0.411872 0.713384i
\(45\) 0 0
\(46\) −2.96410 5.13397i −0.437033 0.756963i
\(47\) −4.76028 8.24504i −0.694358 1.20266i −0.970397 0.241517i \(-0.922355\pi\)
0.276039 0.961147i \(-0.410978\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.633975 + 1.09808i 0.0896575 + 0.155291i
\(51\) 0 0
\(52\) 2.44949 0.339683
\(53\) 1.63397 + 2.83013i 0.224444 + 0.388748i 0.956152 0.292870i \(-0.0946102\pi\)
−0.731709 + 0.681617i \(0.761277\pi\)
\(54\) 0 0
\(55\) −10.5558 −1.42335
\(56\) 0 0
\(57\) 0 0
\(58\) 0.732051 0.0961230
\(59\) 2.50026 4.33057i 0.325506 0.563793i −0.656109 0.754666i \(-0.727799\pi\)
0.981615 + 0.190874i \(0.0611321\pi\)
\(60\) 0 0
\(61\) 1.48356 + 2.56961i 0.189951 + 0.329005i 0.945234 0.326394i \(-0.105834\pi\)
−0.755283 + 0.655399i \(0.772500\pi\)
\(62\) −7.34847 −0.933257
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.36603 4.09808i −0.293469 0.508304i
\(66\) 0 0
\(67\) 7.09808 12.2942i 0.867168 1.50198i 0.00228979 0.999997i \(-0.499271\pi\)
0.864878 0.501982i \(-0.167396\pi\)
\(68\) −6.31319 −0.765587
\(69\) 0 0
\(70\) 0 0
\(71\) 11.1962 1.32874 0.664369 0.747404i \(-0.268700\pi\)
0.664369 + 0.747404i \(0.268700\pi\)
\(72\) 0 0
\(73\) −4.76028 8.24504i −0.557148 0.965009i −0.997733 0.0672983i \(-0.978562\pi\)
0.440584 0.897711i \(-0.354771\pi\)
\(74\) −8.00000 −0.929981
\(75\) 0 0
\(76\) 0.965926 + 1.67303i 0.110799 + 0.191910i
\(77\) 0 0
\(78\) 0 0
\(79\) 5.06218 + 8.76795i 0.569540 + 0.986471i 0.996611 + 0.0822537i \(0.0262118\pi\)
−0.427072 + 0.904218i \(0.640455\pi\)
\(80\) −0.965926 1.67303i −0.107994 0.187051i
\(81\) 0 0
\(82\) 2.82843 4.89898i 0.312348 0.541002i
\(83\) −4.94975 + 8.57321i −0.543305 + 0.941033i 0.455406 + 0.890284i \(0.349494\pi\)
−0.998711 + 0.0507487i \(0.983839\pi\)
\(84\) 0 0
\(85\) 6.09808 + 10.5622i 0.661429 + 1.14563i
\(86\) −1.80385 −0.194514
\(87\) 0 0
\(88\) −5.46410 −0.582475
\(89\) 6.64136 11.5032i 0.703983 1.21933i −0.263074 0.964776i \(-0.584736\pi\)
0.967057 0.254559i \(-0.0819302\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −2.96410 + 5.13397i −0.309029 + 0.535254i
\(93\) 0 0
\(94\) −4.76028 + 8.24504i −0.490985 + 0.850411i
\(95\) 1.86603 3.23205i 0.191450 0.331601i
\(96\) 0 0
\(97\) −1.93185 + 3.34607i −0.196150 + 0.339741i −0.947277 0.320416i \(-0.896177\pi\)
0.751127 + 0.660158i \(0.229511\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.633975 1.09808i 0.0633975 0.109808i
\(101\) 1.55291 0.154521 0.0772604 0.997011i \(-0.475383\pi\)
0.0772604 + 0.997011i \(0.475383\pi\)
\(102\) 0 0
\(103\) 8.38375 0.826075 0.413037 0.910714i \(-0.364468\pi\)
0.413037 + 0.910714i \(0.364468\pi\)
\(104\) −1.22474 2.12132i −0.120096 0.208013i
\(105\) 0 0
\(106\) 1.63397 2.83013i 0.158706 0.274886i
\(107\) 8.46410 14.6603i 0.818256 1.41726i −0.0887109 0.996057i \(-0.528275\pi\)
0.906966 0.421203i \(-0.138392\pi\)
\(108\) 0 0
\(109\) 10.2942 + 17.8301i 0.986008 + 1.70782i 0.637367 + 0.770560i \(0.280023\pi\)
0.348641 + 0.937256i \(0.386643\pi\)
\(110\) 5.27792 + 9.14162i 0.503230 + 0.871619i
\(111\) 0 0
\(112\) 0 0
\(113\) 1.33013 + 2.30385i 0.125128 + 0.216728i 0.921783 0.387706i \(-0.126733\pi\)
−0.796655 + 0.604434i \(0.793399\pi\)
\(114\) 0 0
\(115\) 11.4524 1.06794
\(116\) −0.366025 0.633975i −0.0339846 0.0588631i
\(117\) 0 0
\(118\) −5.00052 −0.460335
\(119\) 0 0
\(120\) 0 0
\(121\) 18.8564 1.71422
\(122\) 1.48356 2.56961i 0.134316 0.232641i
\(123\) 0 0
\(124\) 3.67423 + 6.36396i 0.329956 + 0.571501i
\(125\) −12.1087 −1.08304
\(126\) 0 0
\(127\) 7.92820 0.703514 0.351757 0.936091i \(-0.385584\pi\)
0.351757 + 0.936091i \(0.385584\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −2.36603 + 4.09808i −0.207514 + 0.359425i
\(131\) −0.240237 −0.0209896 −0.0104948 0.999945i \(-0.503341\pi\)
−0.0104948 + 0.999945i \(0.503341\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −14.1962 −1.22636
\(135\) 0 0
\(136\) 3.15660 + 5.46739i 0.270676 + 0.468824i
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) −0.915158 1.58510i −0.0776227 0.134446i 0.824601 0.565715i \(-0.191400\pi\)
−0.902224 + 0.431268i \(0.858066\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −5.59808 9.69615i −0.469780 0.813683i
\(143\) 6.69213 + 11.5911i 0.559624 + 0.969297i
\(144\) 0 0
\(145\) −0.707107 + 1.22474i −0.0587220 + 0.101710i
\(146\) −4.76028 + 8.24504i −0.393963 + 0.682365i
\(147\) 0 0
\(148\) 4.00000 + 6.92820i 0.328798 + 0.569495i
\(149\) −18.3923 −1.50676 −0.753378 0.657588i \(-0.771577\pi\)
−0.753378 + 0.657588i \(0.771577\pi\)
\(150\) 0 0
\(151\) 3.39230 0.276062 0.138031 0.990428i \(-0.455923\pi\)
0.138031 + 0.990428i \(0.455923\pi\)
\(152\) 0.965926 1.67303i 0.0783469 0.135701i
\(153\) 0 0
\(154\) 0 0
\(155\) 7.09808 12.2942i 0.570131 0.987496i
\(156\) 0 0
\(157\) −12.1781 + 21.0931i −0.971918 + 1.68341i −0.282166 + 0.959366i \(0.591053\pi\)
−0.689752 + 0.724046i \(0.742280\pi\)
\(158\) 5.06218 8.76795i 0.402725 0.697541i
\(159\) 0 0
\(160\) −0.965926 + 1.67303i −0.0763631 + 0.132265i
\(161\) 0 0
\(162\) 0 0
\(163\) 10.4641 18.1244i 0.819612 1.41961i −0.0863569 0.996264i \(-0.527523\pi\)
0.905969 0.423345i \(-0.139144\pi\)
\(164\) −5.65685 −0.441726
\(165\) 0 0
\(166\) 9.89949 0.768350
\(167\) −8.05558 13.9527i −0.623359 1.07969i −0.988856 0.148877i \(-0.952434\pi\)
0.365497 0.930813i \(-0.380899\pi\)
\(168\) 0 0
\(169\) 3.50000 6.06218i 0.269231 0.466321i
\(170\) 6.09808 10.5622i 0.467701 0.810082i
\(171\) 0 0
\(172\) 0.901924 + 1.56218i 0.0687710 + 0.119115i
\(173\) −7.26054 12.5756i −0.552008 0.956107i −0.998130 0.0611340i \(-0.980528\pi\)
0.446121 0.894973i \(-0.352805\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.73205 + 4.73205i 0.205936 + 0.356692i
\(177\) 0 0
\(178\) −13.2827 −0.995582
\(179\) 1.09808 + 1.90192i 0.0820741 + 0.142156i 0.904141 0.427235i \(-0.140512\pi\)
−0.822067 + 0.569391i \(0.807179\pi\)
\(180\) 0 0
\(181\) −8.72552 −0.648563 −0.324281 0.945961i \(-0.605122\pi\)
−0.324281 + 0.945961i \(0.605122\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 5.92820 0.437033
\(185\) 7.72741 13.3843i 0.568130 0.984030i
\(186\) 0 0
\(187\) −17.2480 29.8744i −1.26130 2.18463i
\(188\) 9.52056 0.694358
\(189\) 0 0
\(190\) −3.73205 −0.270751
\(191\) 1.59808 + 2.76795i 0.115633 + 0.200282i 0.918033 0.396505i \(-0.129777\pi\)
−0.802400 + 0.596787i \(0.796444\pi\)
\(192\) 0 0
\(193\) 10.1340 17.5526i 0.729459 1.26346i −0.227652 0.973742i \(-0.573105\pi\)
0.957112 0.289718i \(-0.0935617\pi\)
\(194\) 3.86370 0.277398
\(195\) 0 0
\(196\) 0 0
\(197\) 7.66025 0.545771 0.272885 0.962047i \(-0.412022\pi\)
0.272885 + 0.962047i \(0.412022\pi\)
\(198\) 0 0
\(199\) 1.55291 + 2.68973i 0.110083 + 0.190670i 0.915804 0.401626i \(-0.131555\pi\)
−0.805720 + 0.592296i \(0.798222\pi\)
\(200\) −1.26795 −0.0896575
\(201\) 0 0
\(202\) −0.776457 1.34486i −0.0546313 0.0946242i
\(203\) 0 0
\(204\) 0 0
\(205\) 5.46410 + 9.46410i 0.381629 + 0.661002i
\(206\) −4.19187 7.26054i −0.292062 0.505866i
\(207\) 0 0
\(208\) −1.22474 + 2.12132i −0.0849208 + 0.147087i
\(209\) −5.27792 + 9.14162i −0.365081 + 0.632339i
\(210\) 0 0
\(211\) −2.36603 4.09808i −0.162884 0.282123i 0.773018 0.634384i \(-0.218746\pi\)
−0.935902 + 0.352261i \(0.885413\pi\)
\(212\) −3.26795 −0.224444
\(213\) 0 0
\(214\) −16.9282 −1.15719
\(215\) 1.74238 3.01790i 0.118830 0.205819i
\(216\) 0 0
\(217\) 0 0
\(218\) 10.2942 17.8301i 0.697213 1.20761i
\(219\) 0 0
\(220\) 5.27792 9.14162i 0.355837 0.616328i
\(221\) 7.73205 13.3923i 0.520114 0.900864i
\(222\) 0 0
\(223\) 10.3664 17.9551i 0.694183 1.20236i −0.276272 0.961079i \(-0.589099\pi\)
0.970455 0.241281i \(-0.0775676\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.33013 2.30385i 0.0884787 0.153250i
\(227\) −0.896575 −0.0595078 −0.0297539 0.999557i \(-0.509472\pi\)
−0.0297539 + 0.999557i \(0.509472\pi\)
\(228\) 0 0
\(229\) −18.0430 −1.19232 −0.596158 0.802867i \(-0.703307\pi\)
−0.596158 + 0.802867i \(0.703307\pi\)
\(230\) −5.72620 9.91808i −0.377575 0.653979i
\(231\) 0 0
\(232\) −0.366025 + 0.633975i −0.0240307 + 0.0416225i
\(233\) −9.69615 + 16.7942i −0.635216 + 1.10023i 0.351253 + 0.936280i \(0.385756\pi\)
−0.986469 + 0.163946i \(0.947578\pi\)
\(234\) 0 0
\(235\) −9.19615 15.9282i −0.599891 1.03904i
\(236\) 2.50026 + 4.33057i 0.162753 + 0.281896i
\(237\) 0 0
\(238\) 0 0
\(239\) −2.76795 4.79423i −0.179044 0.310113i 0.762510 0.646977i \(-0.223967\pi\)
−0.941553 + 0.336864i \(0.890634\pi\)
\(240\) 0 0
\(241\) 12.7279 0.819878 0.409939 0.912113i \(-0.365550\pi\)
0.409939 + 0.912113i \(0.365550\pi\)
\(242\) −9.42820 16.3301i −0.606068 1.04974i
\(243\) 0 0
\(244\) −2.96713 −0.189951
\(245\) 0 0
\(246\) 0 0
\(247\) −4.73205 −0.301093
\(248\) 3.67423 6.36396i 0.233314 0.404112i
\(249\) 0 0
\(250\) 6.05437 + 10.4865i 0.382912 + 0.663223i
\(251\) −1.93185 −0.121937 −0.0609687 0.998140i \(-0.519419\pi\)
−0.0609687 + 0.998140i \(0.519419\pi\)
\(252\) 0 0
\(253\) −32.3923 −2.03649
\(254\) −3.96410 6.86603i −0.248730 0.430813i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 20.7327 1.29327 0.646636 0.762799i \(-0.276175\pi\)
0.646636 + 0.762799i \(0.276175\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 4.73205 0.293469
\(261\) 0 0
\(262\) 0.120118 + 0.208051i 0.00742094 + 0.0128534i
\(263\) 14.6603 0.903990 0.451995 0.892020i \(-0.350712\pi\)
0.451995 + 0.892020i \(0.350712\pi\)
\(264\) 0 0
\(265\) 3.15660 + 5.46739i 0.193908 + 0.335859i
\(266\) 0 0
\(267\) 0 0
\(268\) 7.09808 + 12.2942i 0.433584 + 0.750990i
\(269\) −0.0185824 0.0321856i −0.00113299 0.00196239i 0.865458 0.500981i \(-0.167027\pi\)
−0.866591 + 0.499018i \(0.833694\pi\)
\(270\) 0 0
\(271\) −2.50026 + 4.33057i −0.151880 + 0.263064i −0.931919 0.362668i \(-0.881866\pi\)
0.780039 + 0.625731i \(0.215199\pi\)
\(272\) 3.15660 5.46739i 0.191397 0.331509i
\(273\) 0 0
\(274\) 0 0
\(275\) 6.92820 0.417786
\(276\) 0 0
\(277\) −5.80385 −0.348719 −0.174360 0.984682i \(-0.555786\pi\)
−0.174360 + 0.984682i \(0.555786\pi\)
\(278\) −0.915158 + 1.58510i −0.0548875 + 0.0950680i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.69615 2.93782i 0.101184 0.175256i −0.810989 0.585062i \(-0.801070\pi\)
0.912173 + 0.409806i \(0.134404\pi\)
\(282\) 0 0
\(283\) −8.55463 + 14.8171i −0.508520 + 0.880783i 0.491431 + 0.870916i \(0.336474\pi\)
−0.999951 + 0.00986623i \(0.996859\pi\)
\(284\) −5.59808 + 9.69615i −0.332185 + 0.575361i
\(285\) 0 0
\(286\) 6.69213 11.5911i 0.395714 0.685397i
\(287\) 0 0
\(288\) 0 0
\(289\) −11.4282 + 19.7942i −0.672247 + 1.16437i
\(290\) 1.41421 0.0830455
\(291\) 0 0
\(292\) 9.52056 0.557148
\(293\) 2.19067 + 3.79435i 0.127980 + 0.221668i 0.922894 0.385054i \(-0.125817\pi\)
−0.794914 + 0.606723i \(0.792484\pi\)
\(294\) 0 0
\(295\) 4.83013 8.36603i 0.281221 0.487089i
\(296\) 4.00000 6.92820i 0.232495 0.402694i
\(297\) 0 0
\(298\) 9.19615 + 15.9282i 0.532719 + 0.922696i
\(299\) −7.26054 12.5756i −0.419888 0.727267i
\(300\) 0 0
\(301\) 0 0
\(302\) −1.69615 2.93782i −0.0976026 0.169053i
\(303\) 0 0
\(304\) −1.93185 −0.110799
\(305\) 2.86603 + 4.96410i 0.164108 + 0.284244i
\(306\) 0 0
\(307\) −29.0793 −1.65964 −0.829822 0.558028i \(-0.811558\pi\)
−0.829822 + 0.558028i \(0.811558\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −14.1962 −0.806287
\(311\) −10.5051 + 18.1953i −0.595688 + 1.03176i 0.397762 + 0.917489i \(0.369787\pi\)
−0.993449 + 0.114273i \(0.963546\pi\)
\(312\) 0 0
\(313\) 0.896575 + 1.55291i 0.0506774 + 0.0877759i 0.890251 0.455470i \(-0.150529\pi\)
−0.839574 + 0.543245i \(0.817195\pi\)
\(314\) 24.3562 1.37450
\(315\) 0 0
\(316\) −10.1244 −0.569540
\(317\) 0.705771 + 1.22243i 0.0396401 + 0.0686586i 0.885165 0.465278i \(-0.154046\pi\)
−0.845525 + 0.533936i \(0.820712\pi\)
\(318\) 0 0
\(319\) 2.00000 3.46410i 0.111979 0.193952i
\(320\) 1.93185 0.107994
\(321\) 0 0
\(322\) 0 0
\(323\) 12.1962 0.678612
\(324\) 0 0
\(325\) 1.55291 + 2.68973i 0.0861402 + 0.149199i
\(326\) −20.9282 −1.15911
\(327\) 0 0
\(328\) 2.82843 + 4.89898i 0.156174 + 0.270501i
\(329\) 0 0
\(330\) 0 0
\(331\) −13.0263 22.5622i −0.715989 1.24013i −0.962577 0.271009i \(-0.912643\pi\)
0.246588 0.969120i \(-0.420691\pi\)
\(332\) −4.94975 8.57321i −0.271653 0.470516i
\(333\) 0 0
\(334\) −8.05558 + 13.9527i −0.440782 + 0.763456i
\(335\) 13.7124 23.7506i 0.749190 1.29764i
\(336\) 0 0
\(337\) −6.66025 11.5359i −0.362807 0.628400i 0.625615 0.780132i \(-0.284848\pi\)
−0.988422 + 0.151732i \(0.951515\pi\)
\(338\) −7.00000 −0.380750
\(339\) 0 0
\(340\) −12.1962 −0.661429
\(341\) −20.0764 + 34.7733i −1.08720 + 1.88308i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.901924 1.56218i 0.0486285 0.0842270i
\(345\) 0 0
\(346\) −7.26054 + 12.5756i −0.390329 + 0.676069i
\(347\) −16.8564 + 29.1962i −0.904899 + 1.56733i −0.0838470 + 0.996479i \(0.526721\pi\)
−0.821052 + 0.570853i \(0.806613\pi\)
\(348\) 0 0
\(349\) 12.3998 21.4770i 0.663744 1.14964i −0.315881 0.948799i \(-0.602300\pi\)
0.979624 0.200839i \(-0.0643667\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.73205 4.73205i 0.145619 0.252219i
\(353\) −19.6975 −1.04839 −0.524195 0.851598i \(-0.675634\pi\)
−0.524195 + 0.851598i \(0.675634\pi\)
\(354\) 0 0
\(355\) 21.6293 1.14796
\(356\) 6.64136 + 11.5032i 0.351992 + 0.609667i
\(357\) 0 0
\(358\) 1.09808 1.90192i 0.0580351 0.100520i
\(359\) −0.0358984 + 0.0621778i −0.00189464 + 0.00328162i −0.866971 0.498358i \(-0.833936\pi\)
0.865077 + 0.501640i \(0.167270\pi\)
\(360\) 0 0
\(361\) 7.63397 + 13.2224i 0.401788 + 0.695917i
\(362\) 4.36276 + 7.55652i 0.229302 + 0.397162i
\(363\) 0 0
\(364\) 0 0
\(365\) −9.19615 15.9282i −0.481349 0.833720i
\(366\) 0 0
\(367\) 14.4195 0.752694 0.376347 0.926479i \(-0.377180\pi\)
0.376347 + 0.926479i \(0.377180\pi\)
\(368\) −2.96410 5.13397i −0.154514 0.267627i
\(369\) 0 0
\(370\) −15.4548 −0.803457
\(371\) 0 0
\(372\) 0 0
\(373\) −5.12436 −0.265329 −0.132665 0.991161i \(-0.542353\pi\)
−0.132665 + 0.991161i \(0.542353\pi\)
\(374\) −17.2480 + 29.8744i −0.891871 + 1.54477i
\(375\) 0 0
\(376\) −4.76028 8.24504i −0.245493 0.425206i
\(377\) 1.79315 0.0923520
\(378\) 0 0
\(379\) 17.5167 0.899770 0.449885 0.893086i \(-0.351465\pi\)
0.449885 + 0.893086i \(0.351465\pi\)
\(380\) 1.86603 + 3.23205i 0.0957251 + 0.165801i
\(381\) 0 0
\(382\) 1.59808 2.76795i 0.0817647 0.141621i
\(383\) 19.5216 0.997507 0.498753 0.866744i \(-0.333791\pi\)
0.498753 + 0.866744i \(0.333791\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −20.2679 −1.03161
\(387\) 0 0
\(388\) −1.93185 3.34607i −0.0980749 0.169871i
\(389\) 29.1244 1.47666 0.738332 0.674438i \(-0.235614\pi\)
0.738332 + 0.674438i \(0.235614\pi\)
\(390\) 0 0
\(391\) 18.7129 + 32.4118i 0.946354 + 1.63913i
\(392\) 0 0
\(393\) 0 0
\(394\) −3.83013 6.63397i −0.192959 0.334215i
\(395\) 9.77938 + 16.9384i 0.492054 + 0.852262i
\(396\) 0 0
\(397\) −0.947343 + 1.64085i −0.0475458 + 0.0823518i −0.888819 0.458259i \(-0.848473\pi\)
0.841273 + 0.540610i \(0.181807\pi\)
\(398\) 1.55291 2.68973i 0.0778406 0.134824i
\(399\) 0 0
\(400\) 0.633975 + 1.09808i 0.0316987 + 0.0549038i
\(401\) −13.0526 −0.651814 −0.325907 0.945402i \(-0.605670\pi\)
−0.325907 + 0.945402i \(0.605670\pi\)
\(402\) 0 0
\(403\) −18.0000 −0.896644
\(404\) −0.776457 + 1.34486i −0.0386302 + 0.0669094i
\(405\) 0 0
\(406\) 0 0
\(407\) −21.8564 + 37.8564i −1.08338 + 1.87647i
\(408\) 0 0
\(409\) 13.1440 22.7661i 0.649930 1.12571i −0.333209 0.942853i \(-0.608131\pi\)
0.983139 0.182859i \(-0.0585352\pi\)
\(410\) 5.46410 9.46410i 0.269853 0.467399i
\(411\) 0 0
\(412\) −4.19187 + 7.26054i −0.206519 + 0.357701i
\(413\) 0 0
\(414\) 0 0
\(415\) −9.56218 + 16.5622i −0.469389 + 0.813005i
\(416\) 2.44949 0.120096
\(417\) 0 0
\(418\) 10.5558 0.516303
\(419\) 2.13990 + 3.70642i 0.104541 + 0.181070i 0.913551 0.406725i \(-0.133329\pi\)
−0.809010 + 0.587796i \(0.799996\pi\)
\(420\) 0 0
\(421\) 5.02628 8.70577i 0.244966 0.424293i −0.717156 0.696913i \(-0.754557\pi\)
0.962122 + 0.272619i \(0.0878899\pi\)
\(422\) −2.36603 + 4.09808i −0.115176 + 0.199491i
\(423\) 0 0
\(424\) 1.63397 + 2.83013i 0.0793528 + 0.137443i
\(425\) −4.00240 6.93237i −0.194145 0.336269i
\(426\) 0 0
\(427\) 0 0
\(428\) 8.46410 + 14.6603i 0.409128 + 0.708630i
\(429\) 0 0
\(430\) −3.48477 −0.168050
\(431\) 7.39230 + 12.8038i 0.356075 + 0.616740i 0.987301 0.158859i \(-0.0507815\pi\)
−0.631226 + 0.775599i \(0.717448\pi\)
\(432\) 0 0
\(433\) 28.7375 1.38104 0.690519 0.723314i \(-0.257382\pi\)
0.690519 + 0.723314i \(0.257382\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −20.5885 −0.986008
\(437\) 5.72620 9.91808i 0.273922 0.474446i
\(438\) 0 0
\(439\) 0.656339 + 1.13681i 0.0313253 + 0.0542571i 0.881263 0.472626i \(-0.156694\pi\)
−0.849938 + 0.526883i \(0.823361\pi\)
\(440\) −10.5558 −0.503230
\(441\) 0 0
\(442\) −15.4641 −0.735552
\(443\) 7.49038 + 12.9737i 0.355879 + 0.616400i 0.987268 0.159066i \(-0.0508483\pi\)
−0.631389 + 0.775466i \(0.717515\pi\)
\(444\) 0 0
\(445\) 12.8301 22.2224i 0.608206 1.05344i
\(446\) −20.7327 −0.981723
\(447\) 0 0
\(448\) 0 0
\(449\) −17.7846 −0.839308 −0.419654 0.907684i \(-0.637849\pi\)
−0.419654 + 0.907684i \(0.637849\pi\)
\(450\) 0 0
\(451\) −15.4548 26.7685i −0.727739 1.26048i
\(452\) −2.66025 −0.125128
\(453\) 0 0
\(454\) 0.448288 + 0.776457i 0.0210392 + 0.0364409i
\(455\) 0 0
\(456\) 0 0
\(457\) 12.8660 + 22.2846i 0.601847 + 1.04243i 0.992541 + 0.121909i \(0.0389017\pi\)
−0.390694 + 0.920521i \(0.627765\pi\)
\(458\) 9.02150 + 15.6257i 0.421547 + 0.730141i
\(459\) 0 0
\(460\) −5.72620 + 9.91808i −0.266986 + 0.462433i
\(461\) 10.9162 18.9074i 0.508418 0.880605i −0.491535 0.870858i \(-0.663564\pi\)
0.999952 0.00974723i \(-0.00310269\pi\)
\(462\) 0 0
\(463\) 5.33013 + 9.23205i 0.247712 + 0.429050i 0.962891 0.269892i \(-0.0869880\pi\)
−0.715179 + 0.698942i \(0.753655\pi\)
\(464\) 0.732051 0.0339846
\(465\) 0 0
\(466\) 19.3923 0.898331
\(467\) −2.39872 + 4.15471i −0.111000 + 0.192257i −0.916174 0.400782i \(-0.868739\pi\)
0.805174 + 0.593039i \(0.202072\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −9.19615 + 15.9282i −0.424187 + 0.734713i
\(471\) 0 0
\(472\) 2.50026 4.33057i 0.115084 0.199331i
\(473\) −4.92820 + 8.53590i −0.226599 + 0.392481i
\(474\) 0 0
\(475\) −1.22474 + 2.12132i −0.0561951 + 0.0973329i
\(476\) 0 0
\(477\) 0 0
\(478\) −2.76795 + 4.79423i −0.126603 + 0.219283i
\(479\) −16.1112 −0.736137 −0.368069 0.929799i \(-0.619981\pi\)
−0.368069 + 0.929799i \(0.619981\pi\)
\(480\) 0 0
\(481\) −19.5959 −0.893497
\(482\) −6.36396 11.0227i −0.289870 0.502070i
\(483\) 0 0
\(484\) −9.42820 + 16.3301i −0.428555 + 0.742279i
\(485\) −3.73205 + 6.46410i −0.169464 + 0.293520i
\(486\) 0 0
\(487\) −1.16025 2.00962i −0.0525761 0.0910645i 0.838540 0.544841i \(-0.183410\pi\)
−0.891116 + 0.453776i \(0.850077\pi\)
\(488\) 1.48356 + 2.56961i 0.0671578 + 0.116321i
\(489\) 0 0
\(490\) 0 0
\(491\) −9.46410 16.3923i −0.427109 0.739774i 0.569506 0.821987i \(-0.307135\pi\)
−0.996615 + 0.0822129i \(0.973801\pi\)
\(492\) 0 0
\(493\) −4.62158 −0.208145
\(494\) 2.36603 + 4.09808i 0.106453 + 0.184381i
\(495\) 0 0
\(496\) −7.34847 −0.329956
\(497\) 0 0
\(498\) 0 0
\(499\) −27.3205 −1.22303 −0.611517 0.791231i \(-0.709440\pi\)
−0.611517 + 0.791231i \(0.709440\pi\)
\(500\) 6.05437 10.4865i 0.270760 0.468970i
\(501\) 0 0
\(502\) 0.965926 + 1.67303i 0.0431114 + 0.0746711i
\(503\) −19.1427 −0.853529 −0.426764 0.904363i \(-0.640347\pi\)
−0.426764 + 0.904363i \(0.640347\pi\)
\(504\) 0 0
\(505\) 3.00000 0.133498
\(506\) 16.1962 + 28.0526i 0.720007 + 1.24709i
\(507\) 0 0
\(508\) −3.96410 + 6.86603i −0.175879 + 0.304631i
\(509\) −21.7680 −0.964850 −0.482425 0.875937i \(-0.660244\pi\)
−0.482425 + 0.875937i \(0.660244\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −10.3664 17.9551i −0.457241 0.791964i
\(515\) 16.1962 0.713688
\(516\) 0 0
\(517\) 26.0106 + 45.0518i 1.14395 + 1.98137i
\(518\) 0 0
\(519\) 0 0
\(520\) −2.36603 4.09808i −0.103757 0.179713i
\(521\) −16.2635 28.1691i −0.712515 1.23411i −0.963910 0.266228i \(-0.914223\pi\)
0.251395 0.967885i \(-0.419111\pi\)
\(522\) 0 0
\(523\) −3.70642 + 6.41971i −0.162070 + 0.280714i −0.935611 0.353032i \(-0.885151\pi\)
0.773541 + 0.633747i \(0.218484\pi\)
\(524\) 0.120118 0.208051i 0.00524739 0.00908875i
\(525\) 0 0
\(526\) −7.33013 12.6962i −0.319609 0.553579i
\(527\) 46.3923 2.02088
\(528\) 0 0
\(529\) 12.1436 0.527982
\(530\) 3.15660 5.46739i 0.137114 0.237488i
\(531\) 0 0
\(532\) 0 0
\(533\) 6.92820 12.0000i 0.300094 0.519778i
\(534\) 0 0
\(535\) 16.3514 28.3214i 0.706932 1.22444i
\(536\) 7.09808 12.2942i 0.306590 0.531030i
\(537\) 0 0
\(538\) −0.0185824 + 0.0321856i −0.000801143 + 0.00138762i
\(539\) 0 0
\(540\) 0 0
\(541\) −8.63397 + 14.9545i −0.371204 + 0.642943i −0.989751 0.142804i \(-0.954388\pi\)
0.618547 + 0.785747i \(0.287721\pi\)
\(542\) 5.00052 0.214791
\(543\) 0 0
\(544\) −6.31319 −0.270676
\(545\) 19.8869 + 34.4452i 0.851862 + 1.47547i
\(546\) 0 0
\(547\) 2.26795 3.92820i 0.0969705 0.167958i −0.813459 0.581623i \(-0.802418\pi\)
0.910429 + 0.413665i \(0.135751\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −3.46410 6.00000i −0.147710 0.255841i
\(551\) 0.707107 + 1.22474i 0.0301238 + 0.0521759i
\(552\) 0 0
\(553\) 0 0
\(554\) 2.90192 + 5.02628i 0.123291 + 0.213546i
\(555\) 0 0
\(556\) 1.83032 0.0776227
\(557\) 13.5622 + 23.4904i 0.574648 + 0.995319i 0.996080 + 0.0884593i \(0.0281943\pi\)
−0.421432 + 0.906860i \(0.638472\pi\)
\(558\) 0 0
\(559\) −4.41851 −0.186883
\(560\) 0 0
\(561\) 0 0
\(562\) −3.39230 −0.143096
\(563\) −4.31199 + 7.46859i −0.181729 + 0.314763i −0.942469 0.334293i \(-0.891503\pi\)
0.760741 + 0.649056i \(0.224836\pi\)
\(564\) 0 0
\(565\) 2.56961 + 4.45069i 0.108104 + 0.187242i
\(566\) 17.1093 0.719156
\(567\) 0 0
\(568\) 11.1962 0.469780
\(569\) 6.53590 + 11.3205i 0.273999 + 0.474580i 0.969882 0.243575i \(-0.0783201\pi\)
−0.695883 + 0.718155i \(0.744987\pi\)
\(570\) 0 0
\(571\) −2.00000 + 3.46410i −0.0836974 + 0.144968i −0.904835 0.425762i \(-0.860006\pi\)
0.821138 + 0.570730i \(0.193340\pi\)
\(572\) −13.3843 −0.559624
\(573\) 0 0
\(574\) 0 0
\(575\) −7.51666 −0.313466
\(576\) 0 0
\(577\) 8.90138 + 15.4176i 0.370569 + 0.641845i 0.989653 0.143480i \(-0.0458292\pi\)
−0.619084 + 0.785325i \(0.712496\pi\)
\(578\) 22.8564 0.950701
\(579\) 0 0
\(580\) −0.707107 1.22474i −0.0293610 0.0508548i
\(581\) 0 0
\(582\) 0 0
\(583\) −8.92820 15.4641i −0.369768 0.640458i
\(584\) −4.76028 8.24504i −0.196982 0.341182i
\(585\) 0 0
\(586\) 2.19067 3.79435i 0.0904958 0.156743i
\(587\) −16.6102 + 28.7697i −0.685577 + 1.18745i 0.287679 + 0.957727i \(0.407117\pi\)
−0.973255 + 0.229727i \(0.926217\pi\)
\(588\) 0 0
\(589\) −7.09808 12.2942i −0.292471 0.506575i
\(590\) −9.66025 −0.397706
\(591\) 0 0
\(592\) −8.00000 −0.328798
\(593\) −10.7453 + 18.6114i −0.441257 + 0.764279i −0.997783 0.0665510i \(-0.978801\pi\)
0.556526 + 0.830830i \(0.312134\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.19615 15.9282i 0.376689 0.652445i
\(597\) 0 0
\(598\) −7.26054 + 12.5756i −0.296905 + 0.514255i
\(599\) 4.19615 7.26795i 0.171450 0.296960i −0.767477 0.641077i \(-0.778488\pi\)
0.938927 + 0.344116i \(0.111821\pi\)
\(600\) 0 0
\(601\) 8.72552 15.1130i 0.355921 0.616474i −0.631354 0.775495i \(-0.717500\pi\)
0.987275 + 0.159021i \(0.0508338\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1.69615 + 2.93782i −0.0690155 + 0.119538i
\(605\) 36.4278 1.48100
\(606\) 0 0
\(607\) 12.9038 0.523749 0.261874 0.965102i \(-0.415659\pi\)
0.261874 + 0.965102i \(0.415659\pi\)
\(608\) 0.965926 + 1.67303i 0.0391735 + 0.0678504i
\(609\) 0 0
\(610\) 2.86603 4.96410i 0.116042 0.200991i
\(611\) −11.6603 + 20.1962i −0.471723 + 0.817049i
\(612\) 0 0
\(613\) 19.2224 + 33.2942i 0.776387 + 1.34474i 0.934012 + 0.357242i \(0.116283\pi\)
−0.157625 + 0.987499i \(0.550384\pi\)
\(614\) 14.5397 + 25.1834i 0.586773 + 1.01632i
\(615\) 0 0
\(616\) 0 0
\(617\) 10.8038 + 18.7128i 0.434947 + 0.753349i 0.997291 0.0735534i \(-0.0234339\pi\)
−0.562345 + 0.826903i \(0.690101\pi\)
\(618\) 0 0
\(619\) 14.5582 0.585145 0.292572 0.956243i \(-0.405489\pi\)
0.292572 + 0.956243i \(0.405489\pi\)
\(620\) 7.09808 + 12.2942i 0.285066 + 0.493748i
\(621\) 0 0
\(622\) 21.0101 0.842430
\(623\) 0 0
\(624\) 0 0
\(625\) −17.0526 −0.682102
\(626\) 0.896575 1.55291i 0.0358344 0.0620669i
\(627\) 0 0
\(628\) −12.1781 21.0931i −0.485959 0.841706i
\(629\) 50.5055 2.01379
\(630\) 0 0
\(631\) −28.1244 −1.11961 −0.559806 0.828623i \(-0.689125\pi\)
−0.559806 + 0.828623i \(0.689125\pi\)
\(632\) 5.06218 + 8.76795i 0.201363 + 0.348770i
\(633\) 0 0
\(634\) 0.705771 1.22243i 0.0280298 0.0485490i
\(635\) 15.3161 0.607801
\(636\) 0 0
\(637\) 0 0
\(638\) −4.00000 −0.158362
\(639\) 0 0
\(640\) −0.965926 1.67303i −0.0381816 0.0661324i
\(641\) −35.0526 −1.38449 −0.692246 0.721661i \(-0.743379\pi\)
−0.692246 + 0.721661i \(0.743379\pi\)
\(642\) 0 0
\(643\) −6.50266 11.2629i −0.256440 0.444167i 0.708846 0.705364i \(-0.249216\pi\)
−0.965286 + 0.261197i \(0.915883\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.09808 10.5622i −0.239926 0.415563i
\(647\) −0.568406 0.984508i −0.0223463 0.0387050i 0.854636 0.519228i \(-0.173780\pi\)
−0.876982 + 0.480523i \(0.840447\pi\)
\(648\) 0 0
\(649\) −13.6617 + 23.6627i −0.536267 + 0.928842i
\(650\) 1.55291 2.68973i 0.0609103 0.105500i
\(651\) 0 0
\(652\) 10.4641 + 18.1244i 0.409806 + 0.709805i
\(653\) 6.67949 0.261389 0.130694 0.991423i \(-0.458279\pi\)
0.130694 + 0.991423i \(0.458279\pi\)
\(654\) 0 0
\(655\) −0.464102 −0.0181340
\(656\) 2.82843 4.89898i 0.110432 0.191273i
\(657\) 0 0
\(658\) 0 0
\(659\) −7.43782 + 12.8827i −0.289736 + 0.501838i −0.973747 0.227634i \(-0.926901\pi\)
0.684010 + 0.729472i \(0.260234\pi\)
\(660\) 0 0
\(661\) −16.8504 + 29.1858i −0.655406 + 1.13520i 0.326385 + 0.945237i \(0.394169\pi\)
−0.981792 + 0.189960i \(0.939164\pi\)
\(662\) −13.0263 + 22.5622i −0.506281 + 0.876904i
\(663\) 0 0
\(664\) −4.94975 + 8.57321i −0.192087 + 0.332705i
\(665\) 0 0
\(666\) 0 0
\(667\) −2.16987 + 3.75833i −0.0840178 + 0.145523i
\(668\) 16.1112 0.623359
\(669\) 0 0
\(670\) −27.4249 −1.05951
\(671\) −8.10634 14.0406i −0.312942 0.542031i
\(672\) 0 0
\(673\) −11.0885 + 19.2058i −0.427429 + 0.740328i −0.996644 0.0818605i \(-0.973914\pi\)
0.569215 + 0.822189i \(0.307247\pi\)
\(674\) −6.66025 + 11.5359i −0.256543 + 0.444346i
\(675\) 0 0
\(676\) 3.50000 + 6.06218i 0.134615 + 0.233161i
\(677\) 7.91688 + 13.7124i 0.304270 + 0.527012i 0.977099 0.212787i \(-0.0682541\pi\)
−0.672828 + 0.739799i \(0.734921\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 6.09808 + 10.5622i 0.233851 + 0.405041i
\(681\) 0 0
\(682\) 40.1528 1.53753
\(683\) −17.1962 29.7846i −0.657992 1.13968i −0.981135 0.193326i \(-0.938073\pi\)
0.323142 0.946350i \(-0.395261\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.80385 −0.0687710
\(689\) 4.00240 6.93237i 0.152479 0.264102i
\(690\) 0 0
\(691\) −12.1273 21.0052i −0.461345 0.799074i 0.537683 0.843147i \(-0.319300\pi\)
−0.999028 + 0.0440735i \(0.985966\pi\)
\(692\) 14.5211 0.552008
\(693\) 0 0
\(694\) 33.7128 1.27972
\(695\) −1.76795 3.06218i −0.0670621 0.116155i
\(696\) 0 0
\(697\) −17.8564 + 30.9282i −0.676360 + 1.17149i
\(698\) −24.7995 −0.938675
\(699\) 0 0
\(700\) 0 0
\(701\) −27.4641 −1.03730 −0.518652 0.854985i \(-0.673566\pi\)
−0.518652 + 0.854985i \(0.673566\pi\)
\(702\) 0 0
\(703\) −7.72741 13.3843i −0.291445 0.504797i
\(704\) −5.46410 −0.205936
\(705\) 0 0
\(706\) 9.84873 + 17.0585i 0.370662 + 0.642005i
\(707\) 0 0
\(708\) 0 0
\(709\) 14.7321 + 25.5167i 0.553274 + 0.958298i 0.998036 + 0.0626494i \(0.0199550\pi\)
−0.444762 + 0.895649i \(0.646712\pi\)
\(710\) −10.8147 18.7315i −0.405867 0.702982i
\(711\) 0 0
\(712\) 6.64136 11.5032i 0.248896 0.431100i
\(713\) 21.7816 37.7269i 0.815728 1.41288i
\(714\) 0 0
\(715\) 12.9282 + 22.3923i 0.483487 + 0.837425i
\(716\) −2.19615 −0.0820741
\(717\) 0 0
\(718\) 0.0717968 0.00267943
\(719\) 9.93666 17.2108i 0.370575 0.641855i −0.619079 0.785329i \(-0.712494\pi\)
0.989654 + 0.143474i \(0.0458274\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 7.63397 13.2224i 0.284107 0.492088i
\(723\) 0 0
\(724\) 4.36276 7.55652i 0.162141 0.280836i
\(725\) 0.464102 0.803848i 0.0172363 0.0298541i
\(726\) 0 0
\(727\) −12.0580 + 20.8850i −0.447206 + 0.774583i −0.998203 0.0599240i \(-0.980914\pi\)
0.550997 + 0.834507i \(0.314247\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −9.19615 + 15.9282i −0.340365 + 0.589529i
\(731\) 11.3880 0.421202
\(732\) 0 0
\(733\) 8.06918 0.298042 0.149021 0.988834i \(-0.452388\pi\)
0.149021 + 0.988834i \(0.452388\pi\)
\(734\) −7.20977 12.4877i −0.266117 0.460929i
\(735\) 0 0
\(736\) −2.96410 + 5.13397i −0.109258 + 0.189241i
\(737\) −38.7846 + 67.1769i −1.42865 + 2.47449i
\(738\) 0 0
\(739\) 21.9282 + 37.9808i 0.806642 + 1.39714i 0.915177 + 0.403052i \(0.132051\pi\)
−0.108535 + 0.994093i \(0.534616\pi\)
\(740\) 7.72741 + 13.3843i 0.284065 + 0.492015i
\(741\) 0 0
\(742\) 0 0
\(743\) 10.1244 + 17.5359i 0.371427 + 0.643330i 0.989785 0.142566i \(-0.0455354\pi\)
−0.618359 + 0.785896i \(0.712202\pi\)
\(744\) 0 0
\(745\) −35.5312 −1.30176
\(746\) 2.56218 + 4.43782i 0.0938080 + 0.162480i
\(747\) 0 0
\(748\) 34.4959 1.26130
\(749\) 0 0
\(750\) 0 0
\(751\) 12.1769 0.444342 0.222171 0.975008i \(-0.428686\pi\)
0.222171 + 0.975008i \(0.428686\pi\)
\(752\) −4.76028 + 8.24504i −0.173590 + 0.300666i
\(753\) 0 0
\(754\) −0.896575 1.55291i −0.0326514 0.0565538i
\(755\) 6.55343 0.238504
\(756\) 0 0
\(757\) −28.2487 −1.02672 −0.513358 0.858174i \(-0.671599\pi\)
−0.513358 + 0.858174i \(0.671599\pi\)
\(758\) −8.75833 15.1699i −0.318117 0.550995i
\(759\) 0 0
\(760\) 1.86603 3.23205i 0.0676879 0.117239i
\(761\) 5.48099 0.198686 0.0993428 0.995053i \(-0.468326\pi\)
0.0993428 + 0.995053i \(0.468326\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −3.19615 −0.115633
\(765\) 0 0
\(766\) −9.76079 16.9062i −0.352672 0.610846i
\(767\) −12.2487 −0.442275
\(768\) 0 0
\(769\) 2.20925 + 3.82654i 0.0796677 + 0.137989i 0.903107 0.429416i \(-0.141281\pi\)
−0.823439 + 0.567405i \(0.807947\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10.1340 + 17.5526i 0.364730 + 0.631730i
\(773\) −1.81173 3.13801i −0.0651635 0.112867i 0.831603 0.555371i \(-0.187424\pi\)
−0.896767 + 0.442504i \(0.854090\pi\)
\(774\) 0 0
\(775\) −4.65874 + 8.06918i −0.167347 + 0.289853i
\(776\) −1.93185 + 3.34607i −0.0693494 + 0.120117i
\(777\) 0 0
\(778\) −14.5622 25.2224i −0.522079 0.904268i
\(779\) 10.9282 0.391544
\(780\) 0 0
\(781\) −61.1769 −2.18908
\(782\) 18.7129 32.4118i 0.669174 1.15904i
\(783\) 0 0
\(784\) 0 0
\(785\) −23.5263 + 40.7487i −0.839689 + 1.45438i
\(786\) 0 0
\(787\) −3.95164 + 6.84443i −0.140861 + 0.243978i −0.927821 0.373026i \(-0.878320\pi\)
0.786960 + 0.617004i \(0.211654\pi\)
\(788\) −3.83013 + 6.63397i −0.136443 + 0.236326i
\(789\) 0 0
\(790\) 9.77938 16.9384i 0.347935 0.602640i
\(791\) 0 0
\(792\) 0 0
\(793\) 3.63397 6.29423i 0.129046 0.223515i
\(794\) 1.89469 0.0672399
\(795\) 0